Reverberation is a well known eect that has an important role in our listening experience. Reverberation changes positively the perception of the sound, adding fullness and sense of space. Generally, two approaches are employed for articial reverberation: the desired signal can be obtained by convolving the input signal with a measured impulse response (IR) or by synthetic techniques based on recursive lter structures. Taking into account the advantages of both approaches, a hybrid articial reverberation algorithm is presented aiming to reproduce the acoustic behaviour of real environment with a low computational load. More in detail, the early reflections are derived from a real impulse response, truncated considering the calculated mixing time, and the reverberation tail is obtained using an IIR lter network. The parameters dening this structure are automatically derived from the analyzed impulse response, using a minimization criteria based on Simultaneous Perturbation Stochastic Approximation (SPSA). The effectiveness of the proposed approach has been proved taking into account a real Italian Theatre impulse response providing comparison with the existing state-of-art techniques in terms of objective and subjective measures.

1. Hybrid Reverberation Algorithm:
a Practical Approach
A. Primavera1, M. Gasparini1, S. Cecchi1, L. Romoli1 and F. Piazza1
1
A3Lab - DII - Universit`a Politecnica delle Marche
Via Brecce Bianche 1, 60131 Ancona Italy
www.a3lab.dibet.univpm.it
Abstract
Reverberation is a well known effect that has an important role in our listening experience. Reverber-
ation changes positively the perception of the sound, adding fullness and sense of space. Generally,
two approaches are employed for artificial reverberation: the desired signal can be obtained by con-
volving the input signal with a measured impulse response (IR) or by synthetic techniques based on
recursive filter structures. Taking into account the advantages of both approaches, a hybrid artificial
reverberation algorithm is presented aiming to reproduce the acoustic behaviour of real environment
with a low computational load. More in detail, the early reflections are derived from a real impulse
response, truncated considering the calculated mixing time, and the reverberation tail is obtained
using an IIR filter network. The parameters defining this structure are automatically derived from
the analyzed impulse response, using a minimization criteria based on Simultaneous Perturbation
Stochastic Approximation (SPSA). The effectiveness of the proposed approach has been proved
taking into account a real Italian theatre impulse response providing comparison with the existing
state-of-art techniques in terms of objective and subjective measures.

2. Introduction
Reverberation is probably the most used audio effect employed by musician during live performances
and recording session.
• Synthetic Approach: the reverberation effect is achieved employing IIR structures (e.g., comb
and/or allpass) [1].
Pros: Great flexibility and high computational efficiency.
Cons: Low accuracy.
• Fast Convolution: the desired signal is obtained convolving the input signal with a given IR [2].
Pros: Accurate reproduction of the acoustic environment.
Cons: Computational complexity as a function to the IR length.
• Hybrid Technique: reverberation is obtained taking into account the main advantages of the
aforementioned approaches [5] [6] [7].
Pros: Low computational cost and audio quality comparable to the convolution approach.
Cons: None.
State of the Art
To prove the effectiveness of hybrid reverberation algorithm [7] taking into account a real Italian
theatre impulse response (i.e., Le Muse Theatre of Ancona [11]).
Objective of this work

3. Hybrid Reverberation Algorithm - The Structure
The presented hybrid reverberator [7] is mainly composed of two parts as the Moorer’s reverberator
[4].
+
EARLY
REFLECTIONS
DEVICE
LATE
REFLECTIONS
DEVICE
DELAY ×
x[n] y[n]
gain
Hybrid reverberator block diagram for the single channel case.
Based on the convolution with a real IR for
the reproduction of the early echoes.
Early reflections device
Based on IIR filters network (e.g., comb
and/or all-pass) and a FDN matrix [8] for
the simulation of the reverberation tail.
Late reflections device
LBCF
+
x[n]
LBCF
LBCF
LBCF
AP AP
A
++
++
++
+
+
y[n]
NAP filters
NLBCF filters
Late reflections device block diagram for the single channel
case.
Set the parameters of hybrid reverberator in order to emulate a real environment starting from its
impulse response.
Autotuning procedure

4. Hybrid Reverberation Algorithm - The Autotuning Procedure
An offline procedure has been developed in order to determine all the parameters of the hybrid
reverberation algorithm starting from the IR of a real environment.
Evaluation of the mixing time to set the
Early reflection device:
• Gaussianity estimators: Similarities
between IR behavior and gaussian noise
can be found in late reflections. Kurto-
sis (k) and MAD/SD ratio (r) have been
used.
k =
E (x − µ)4
σ4
− 3 → 0
r =
E (|x − µ|)
σ
→
2
π
• Phase distortion evaluation: The un-
wrapped phase of the IR tends to be-
come not linear with late reflections evo-
lution.
Early Reflections Partitioning
An offline adaptation procedure, based on
SPSA [10], has been used to iteratively find
the parameters set of the IIR structure.
A single loss function computed in cepstral
domain [9] has been adopted in the mini-
mization procedure.
L = max



max



K
i=1
M
j=1
[Tr(i, j) − Ta(i, j)]2






where:
• Tr is a matrix representing the Mel-
Frequency Cepstral Coefficients (MFCC)
derived from the real IR.
• Ta is the MFCC obtained by the artificial
IR.
Late Reflections Analysis

5. Experimental Setup
The effectiveness of the presented technique [7] has been proved taking into account a real Italian
theatre impulse response (i.e., Le Muse Theatre).
Interior view of Le Muse Theatre.
The theatre impulse response has been de-
rived using:
• A logarithmic sweep signal excitation.
• Sample rate of 48kHz.
• Omnidirectional microphone
(Beyer-dynamic MM 1).
• A professional soundcard
(MOTU MICROBOOK).
Different tests have been carried out in order to evaluate the reverberation quality, providing com-
parison with the existing state-of-art techniques in terms of objective and subjective measures also
considering a real-time implementation on an embedded platform.

6. Experimental Results - EDRs and IRs evaluation
0 0.5 1 1.5 2 2.5 3
-1
-0.5
0
0.5
1
Time [sec]
Amplitude
(a)
0 0.5 1 1.5 2 2.5 3
-1
-0.5
0
0.5
1
Time [sec]
Amplitude
(b)
(a) Real impulse response of Le Muse Theatre. (b) Artificial impulse response derived with the proposed approach.
(a) (b)
Energy decay relief. (a) Le Muse Theatre impulse response. (b) Artificial impulse response derived with the proposed approach.

7. Experimental Results - Comparison with Fast Convolution
The presented hybrid reverberation algorithm [7] has been compared with a fast convolution algo-
rithm based on the non uniform partitioning of the IR [3].
A real-time implementation of the presented algorithms has been realized on the OMAPL137 plat-
form (DSP+ARM Texas Instruments) taking into account several design constraints (i.e., stereo im-
plementation, sample rate of 48 kHz, and frame size of 64 samples).
Workload
Hybrid Reverberator [7] 26 %
Fast convolution [3] 36 %
Internal memory
Hybrid Reverberator [7] 10 kB
Fast convolution [3] 100 kB
The obtained results confirm the improvement in terms of required computational resources
achieved using the hybrid reverberation structure.
Consideration
The artificial effect produced using the presented hybrid reverberation algorithms is really similar
to the natural one confirming the effectiveness of the presented approach.
Audio Quality Evaluation

8. Conclusions
• A hybrid reverberation algorithm with an automatic procedure for the parameters setting has been presented.
• The automatic procedure is based on the evaluation of the mixing time and the minimization of a single loss function
computed in the cepstral domain using the SPSA criterium.
• The effectiveness of the presented approach has been proved taking into account a real Italian theatre impulse
response (i.e., Le Muse Theatre of Ancona).
• Different tests have been carried out in order to evaluate the reverberation quality, providing comparison with the
existing state-of-art techniques in terms of objective and subjective measures also considering a real-time imple-
mentation on an embedded platform.
• The hybrid reverberator introduces a remarkable improvement in terms of computational complexity reduction with
respect to fast convolution algorithm.
• As confirmed by informal listening tests the artificial effect generated using the hybrid reverberation algorithm
sounds really similar to the natural one validating the presented approach.
References
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[2] W. G. Gardner, Efficient Convolution without Input-Output Delay, Journal of the Audio Engineering Society, vol. 43, pp. 127136, Mar. 1995.
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Amsterdam, NL, Sep. 2012.
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[10] J.C. Spall, Implementation of the Simultaneous Perturbation Algorithm for Stochastic Optimization, in IEEE Transactions on Aerospace and Electronic Systems, vol. 34, pp. 817-823, 1998.
[11] Reference to the Teatro delle Muse homepage. URL: http://www.teatrodellemuse.org/